What is the general solution for (sin(x)-1)(sin(x)-5)=0 ?

The general solution for (sin(x)-1)(sin(x)-5)=0 is x= pi/2+2pin

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(sin(x)-1)(sin(x)-5)=0

(sin (x) - 1) (sin (x) - 5) = 0

x = \frac{π}{2} + 2 πn

Solution steps

(sin (x) - 1) (sin (x) - 5) = 0

Solving each part separately

sin (x) - 1 = 0 or sin (x) - 5 = 0

sin (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

sin (x) - 5 = 0 :

No Solution

Combine all the solutions

x = \frac{π}{2} + 2 πn

(4 sin^{2} (x) - 1) (cos^{2} (x) - 1) = 0

3 sin^{2} (x) - 6 sin (x) = - 3, 0 \leq x \leq 2 π

1 + sin (π \cdot t) = \frac{3}{2}

- cos (x) = sin^{2} (x) - 1

csc (x) = \frac{5}{2}

What is the general solution for (sin(x)-1)(sin(x)-5)=0 ?
The general solution for (sin(x)-1)(sin(x)-5)=0 is x= pi/2+2pin